The Midpoint of a Line Anne Gilleran.

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Presentation transcript:

The Midpoint of a Line Anne Gilleran

The Midpoint of a Line To learn how to find the midpoint of a line segment Learning Intention

The Midpoint of a Line (Warm Up) 1. +3 + -2 = +1 5. +4 + -6 = -2 2. -3 + -2 = -5 6. -5 + -7 = -12 3. -3 + +1 = -2 7. -2 + +8 = +6 4. +2 + -3 = -1 8. +6 + -9 = -3 3

The Midpoint of a Line What’s half way between each pair of numbers? 1. 2 & 6 4 6. 7 & 10 8.5 2. 4 & 8 6 7. -9 & -5 -7 3. 12 & 20 16 8. -10 & -5 -7.5 4. -3 & 3 9. -11 & 3 -4 5. -2 & 6 2 10. 28 & 50 39 ? ? ? ? ? ? ? ? ? ? 4

This is a line… This is a line segment…

x x Find the midpoint of the lines between.... y y b. (2,6) and (5,2) a. (0,1) and (6,5) b. (2,6) and (5,2) 0 1 2 3 4 5 6 5 4 3 2 1 y x y 5 4 3 2 1 x 0 1 2 3 4 5 6 Can you write a formula for co-ordinates (x1,y1) and (x2,y2) Midpoint at (3,3)

The midpoint of a line x KEY POINT y midpoint at ( , ) The midpoint of a segment is the average of the two x co-ordinates and two y co-ordinates. y 2 + 4 2 x co-ordinate: = (2,5) 5 + 2 2 y co-ordinate: = (4,2) copy down x midpoint at ( , )

The midpoint of a line x KEY POINT y The midpoint of a line between points (x1,y1) and (x2,y2) is... y (x1,y1) x1 + x2 2 y1 + y2 , (x2,y2) copy down x

Find the midpoint of the line segment between points (-3,2) and (2,-3) 1 2 3 -1 -2 -3 Midpoint at x1 + x2 2 y1 + y2 ,

Find the midpoint of the line segments between these sets of points (answer with plickers) 1. (0,3) & (6,5) (3,6) 2. (2,5) (10,9) (6,7) 3. (8,12) (6,10) (7,11) 4. (-3,7) (-5,7) (-4,7) 5. (2,2) (5,10) (3.5,6) 6. (0,-3) (0,5) (0,1) 7. (-7,-10) (-5,60) (-6,25) 8. (-13,-81) (-10,7) (-11.5,-37)

Bonus Questions 1. Find the centre of a square with co-ordinates at A (-4,12), B (8,4), C(0,-8) & (12,0) 2. Two boats begin at the same place. One sails East at 15 nautical miles per hour, the other sails South at the same speed. After 3 hours they turn & begin sailing toward each other. Where do they meet in relation to where they first started?

Q1 ANSWER 4 8 12 -4 -8 -12 Midpoint at (-2,-2)

N E Meet at 22.5 nautical miles East, 22.5 nautical miles South Q2 ANSWER N 15 30 45 Meet at 22.5 nautical miles East, 22.5 nautical miles South E

Find the midpoint of the line between (0,5) and (6,1) PLENARY Find the midpoint of the line between (0,5) and (6,1) y Explain how to find the midpoint of a line segment in one sentence. 5 4 3 2 1 x 0 1 2 3 4 5 6

On mini whiteboards

Find the midpoint of the line segment between.... (3,1) & (2,5) (2.5,3)

Find the midpoint of the line segment between.... (2,9) & (6,2) (4,5.5)

Find the midpoint of the line segment between.... (12,8) & (11,18) (11.5,13)

Find the midpoint of the line segment between.... (-2,-3) & (2,3) (0,0)

Find the midpoint of the line segment between.... (-4,-1) & (6,4) (1,1.5)

Find the midpoint of the line segment between.... (-5,-10) & (-3,-4) (-4,-7)